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LECTURE 10
Forecasting
Forecasting
• Predicting the future• Qualitative forecast methods
• subjective
• Quantitative forecast methods• based on mathematical formulas
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-2
The Effect of Inaccurate Forecasting
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-3
Forecasting
• Quality Management• Accurately forecasting customer demand is a key to
providing good quality service
• Strategic Planning• Successful strategic planning requires accurate
forecasts of future products and markets
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-4
Components of Forecasting Demand
• Time frame• Demand behavior• Causes of behavior
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-5
Time Frame
• Indicates how far into the future is forecast• Short- to mid-range forecast
• typically encompasses the immediate future• daily up to two years
• Long-range forecast• usually encompasses a period of time longer than
two years
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-6
Demand Behavior
• Trend• a gradual, long-term up or down movement of demand
• Random variations• movements in demand that do not follow a pattern
• Cycle• an up-and-down repetitive movement in demand
• Seasonal pattern• an up-and-down repetitive movement in demand
occurring periodically
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-7
Forms of Forecast Movement
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-8
Forecasting Methods
• Time series• statistical techniques that use historical demand data
to predict future demand
• Regression methods• attempt to develop a mathematical relationship
between demand and factors that cause its behavior
• Qualitative• use management judgment, expertise, and opinion to
predict future demand
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-9
Qualitative Methods
• Management, marketing, purchasing, and engineering are sources for internal qualitative forecasts
• Delphi method• involves soliciting forecasts about technological
advances from experts
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-10
Forecasting Process
6. Check forecast accuracy with one or more measures
4. Select a forecast model that seems appropriate for data
5. Develop/compute forecast for period of historical data
8a. Forecast over planning horizon
9. Adjust forecast based on additional qualitative information and insight
10. Monitor results and measure forecast accuracy
8b. Select new forecast model or adjust parameters of existing model
7.Is accuracy of
forecast acceptable?
1. Identify the purpose of forecast
3. Plot data and identify patterns
2. Collect historical data
No
Yes
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-11
Time Series
• Assume that what has occurred in the past will continue to occur in the future
• Relate the forecast to only one factor - time• Include
• naïve forecast• moving average• exponential smoothing• linear trend line
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-12
Moving Average
• Naive forecast• demand in current period is used as next period’s
forecast• Simple moving average
• uses average demand for a fixed sequence of periods• good for stable demand with no pronounced
behavioral patterns• Weighted moving average
• weights are assigned to most recent data
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-13
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-14
Moving Average: Naïve Approach
Jan 120
Feb 90
Mar 100
Apr 75
May 110
June 50
July 75
Aug 130
Sept 110
Oct 90
ORDERSMONTH PER MONTH
Nov -
FORECAST
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-15
Moving Average: Naïve Approach
Jan 120
Feb 90
Mar 100
Apr 75
May 110
June 50
July 75
Aug 130
Sept 110
Oct 90
ORDERSMONTH PER MONTH
-120
90100
751105075
13011090Nov -
FORECAST
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-16
Simple Moving Average
MAn =
n
i = 1 Di
nwhere
n = number of periods in the moving
averageDi = demand in
period i
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-17
3-month Simple Moving Average
Jan 120
Feb 90
Mar 100
Apr 75
May 110
June 50
July 75
Aug 130
Sept 110
Oct 90Nov -
ORDERS
MONTH PER MONTH
MA3 =
3
i = 1 Di
3
MOVING AVERAGE
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-18
3-month Simple Moving Average
Jan 120
Feb 90
Mar 100
Apr 75
May 110
June 50
July 75
Aug 130
Sept 110
Oct 90Nov -
ORDERS
MONTH PER MONTH
MA3 =
3
i = 1 Di
3
=90 + 110 + 130
3
= 110 orders for Nov
–––
103.388.395.078.378.385.0
105.0110.0
MOVING AVERAGE
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-19
5-month Simple Moving Average
MA5 =
5
i = 1 Di
5
Jan 120
Feb 90
Mar 100
Apr 75
May 110
June 50
July 75
Aug 130
Sept 110
Oct 90Nov -
ORDERS
MONTH PER MONTH
MOVING AVERAGE
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-20
5-month Simple Moving Average
MA5 =
5
i = 1 Di
5
=90 + 110 + 130+75+50
5
= 91 orders for Nov
Jan 120
Feb 90
Mar 100
Apr 75
May 110
June 50
July 75
Aug 130
Sept 110
Oct 90Nov -
ORDERS
MONTH PER MONTH –
–– –
– 99.085.082.088.095.091.0
MOVING AVERAGE
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-21
Smoothing Effects
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-22
Weighted Moving Average
• Adjusts moving average method to more closely reflect data fluctuations
WMAn = i = 1 Wi Di
where
Wi = the weight for period i,
between 0 and 100 percent
Wi = 1.00
n
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-23
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-24
Weighted Moving Average Example
MONTH WEIGHT DATA
August 17% 130September 33% 110October 50% 90
WMA3 = 3
i = 1 Wi DiNovember Forecast
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-25
Weighted Moving Average Example
MONTH WEIGHT DATA
August 17% 130September 33% 110October 50% 90
WMA3 = 3
i = 1 Wi Di
= (0.50)(90) + (0.33)(110) + (0.17)(130)
= 103.4 orders
November Forecast
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-26
Exponential Smoothing
• Averaging method • Weights most recent data more strongly• Reacts more to recent changes• Widely used, accurate method• Smoothing constant, α
• applied to most recent data
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-27
Exponential Smoothing
Ft +1 = Dt + (1 - )Ft
where:
Ft +1 = forecast for next period
Dt = actual demand for present period
Ft = previously determined forecast for present period
= weighting factor, smoothing constant
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-28
0.0 1.0
If = 0.20, then Ft +1 = 0.20Dt + 0.80 Ft
If = 0, then Ft +1 = 0Dt + 1 Ft = Ft
Forecast does not reflect recent data
If = 1, then Ft +1 = 1Dt + 0 Ft =Dt Forecast based only on most recent data
Effect of Smoothing Constant
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-29
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-30
Exponential Smoothing (α=0.30)
F2 = D1 + (1 - )F1
F3 = D2 + (1 - )F2
F13 = D12 + (1 - )F12
PERIOD MONTHDEMAND
1 Jan 37
2 Feb 40
3 Mar 41
4 Apr 37
5 May 45
6 Jun 50
7 Jul 43
8 Aug 47
9 Sep 56
10 Oct 52
11 Nov 55
12 Dec 54
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-31
Exponential Smoothing (α=0.30)
F2 = D1 + (1 - )F1
= (0.30)(37) + (0.70)(37)
= 37
F3 = D2 + (1 - )F2
= (0.30)(40) + (0.70)(37)
= 37.9
F13 = D12 + (1 - )F12
= (0.30)(54) + (0.70)(50.84)
= 51.79
PERIOD MONTHDEMAND
1 Jan 37
2 Feb 40
3 Mar 41
4 Apr 37
5 May 45
6 Jun 50
7 Jul 43
8 Aug 47
9 Sep 56
10 Oct 52
11 Nov 55
12 Dec 54
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-32
Exponential SmoothingFORECAST, Ft + 1
PERIOD MONTH DEMAND ( = 0.3) ( = 0.5)
1 Jan 37 – –2 Feb 403 Mar 414 Apr 375 May 456 Jun 507 Jul 438 Aug 479 Sep 56
10 Oct 5211 Nov 5512 Dec 5413 Jan –
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-33
Exponential SmoothingFORECAST, Ft + 1
PERIOD MONTH DEMAND ( = 0.3) ( = 0.5)
1 Jan 37 – –2 Feb 40 37.00 37.003 Mar 41 37.90 38.504 Apr 37 38.83 39.755 May 45 38.28 38.376 Jun 50 40.29 41.687 Jul 43 43.20 45.848 Aug 47 43.14 44.429 Sep 56 44.30 45.71
10 Oct 52 47.81 50.8511 Nov 55 49.06 51.4212 Dec 54 50.84 53.2113 Jan – 51.79 53.61
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-34
Exponential Smoothing
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-35
Forecast Accuracy
• Forecast error• difference between forecast and actual demand
• MAD• mean absolute deviation
• MAPD• mean absolute percent deviation
• Cumulative error• Average error or bias
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-36
Mean Absolute Deviation (MAD)
where t = period number
Dt = demand in period t
Ft = forecast for period t
n = total number of periods = absolute value
S Dt - Ft nMAD =
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-37
MAD Example
1 37 37.00 – –2 40 37.003 41 37.904 37 38.835 45 38.286 50 40.297 43 43.208 47 43.149 56 44.30
10 52 47.8111 55 49.0612 54 50.84
PERIOD DEMAND, Dt Ft ( =0.3) (Dt - Ft) |Dt - Ft|
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-38
MAD Example
1 37 37.00 – –2 40 37.00 3.00 3.003 41 37.90 3.10 3.104 37 38.83 -1.83 1.835 45 38.28 6.72 6.726 50 40.29 9.69 9.697 43 43.20 -0.20 0.208 47 43.14 3.86 3.869 56 44.30 11.70 11.70
10 52 47.81 4.19 4.1911 55 49.06 5.94 5.9412 54 50.84 3.15 3.15
557 49.31 53.39
PERIOD DEMAND, Dt Ft ( =0.3) (Dt - Ft) |Dt - Ft|
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-39
MAD Calculation
S Dt - Ft nMAD =
=
= 4.85
53.3911
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-40
Other Accuracy Measures
Mean absolute percent deviation (MAPD)
MAPD =|Dt - Ft|
Dt
Cumulative error
E = et
Average error
E =et
n
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-41
Comparison of Forecasts
FORECAST MAD MAPD E (E)
Exponential smoothing (= 0.30) 4.85 9.6% 49.31 4.48
Exponential smoothing (= 0.50) 4.04 8.5% 33.21 3.02
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e 12-42
Based on the table, the company should choose 5-month forecast because the smaller MAD indicates a more accurate forecast